For a solution to with and

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

For a solution to

\dfrac{dy}{dt}=ky(a-y)

with

k>0

and

a>0

, describe the concavity of the solution curve when

0<y<\dfrac{a}{2}

and provide a brief reason based on the sign of the appropriate derivative.